Modified TL-subgroups of a group

Abstract

A modified version of a TL-group is proposed, which pushes up the grade of the identity element automatically at the highest level without requiring to peg it under compulsion at as high a point as 1. The study creates a viable level theory even when a general triangular norm on the complete lattice L is present there. It is successfully employed to prove the modularity of the class of all modified TL-subgroups of a given quasi-Hamiltonian group, which are shown to form a complete lattice for which the T-intersection turns out to be the meet operation. The theory opens up a vista of smooth generalization of the fuzzy group, filing off all angularities created by an early introduction of a triangular norm as a technical misfit.